F-regularity and finite generation of monoid algebras determined by convex cones

Conjectures about the finite generation of various classes of rings in function fields have been instrumental in the development of algebraic geometry and commutative algebra. In this talk we will introduce one such conjecture in prime characteristic via a variant of F-regularity, which is a prime characteristic analog of KLT singularities from characteristic 0 birational geometry. We will mention the connection of this problem to other long-standing conjectures in the theory of F-singularities and tight closure. Our main goal is to discuss evidence in favor of the conjecture by considering the class of monoid algebras determined by lattice points inside convex cones of finite dimensional vector spaces. The talk is based on joint work with Karl Schwede and Kevin Tucker.